I have been a counter person and cashier in my own restaurant before and I did give the customers back the wrong change many times. Once customer told me, I would just give back the right change. I would not ask the customer to check their pocket. I think it's rude to do so.
There was once a customer left the change (more than 5 bucks) on the counter and he went to next stall and my wife had to call him back to get the change. We would not take money which is not rightfully ours.
haha. there was in a small cafe near my old office when I was with my old job. I once just took the hamburger and forgot to pay. They knew I was from the office upstairs and kindly reminded us that we forgot to pay....